Chapter 4.2, Problem 4BGP

To determine

To write: An equation in point-slope form and standard form the line containing side $\overline{SR}$ .

Answer to Problem 4BGP

Equation in slope-intercept form is $y=x+4$

Equation in standard form is $x-y=-4.$

Explanation of Solution

Given information: The figure shows square RSTU.

  

Calculation:

The coordinates of point S is (4,8). $(x_2,y_2)$ .

The coordinates of point R is (1,5) $(x_1,y_1)$

So, the slope of the line $\overline{ST}$ is ,

  $m=\frac{y_2-y_1}{x_2-x_1}=\frac{8-5}{4-1}=\frac{3}{3}=1$ .

Substitute the point R(1,5) and the slope m =1 into the slope-intercept form of a line and solve for b .

  $\begin{array}{l}y=mx+b.\\ 5=1\times 1+b.\\ b=5-1=4.\end{array}$

Substitute the slope m =1 and b =4 into slope-intercept form of a line.

  $\begin{array}{l}y=1\times x+4.\\ y=x+4.\end{array}$

So, equation in slope-intercept form is ,

  $y=x+4$

In standard form the equation is ,

  $x-y=-4.$